In this report we consider a new version of the arithmetic mean method for solving large block tridiagonal linear systems. The iterative method converges for systems with symmetric positive definite or positive real matrices or irreducible L-matrices with a strong diagonal dominance. When the coefficient matrix is symmetric positive definite, an additive preconditioner for the conjugate gradient method is derived.The Fortran 77 code carried out on multivector computer Cray Y-MP implementing the algorithm above, are reported in appendix.
V., Ruggiero e Emanuele, Galligani. "A new version of the arithmetic mean method for solving block tridiagonal linear systems" Working paper, CNR, Collana del progetto finalizzato “Sistemi Informatici e Calcolo Parallelo”, sottoprogetto 1 “Calcolo Scientifico per Grandi Sistemi”, 1992.
A new version of the arithmetic mean method for solving block tridiagonal linear systems
GALLIGANI, Emanuele
1992
Abstract
In this report we consider a new version of the arithmetic mean method for solving large block tridiagonal linear systems. The iterative method converges for systems with symmetric positive definite or positive real matrices or irreducible L-matrices with a strong diagonal dominance. When the coefficient matrix is symmetric positive definite, an additive preconditioner for the conjugate gradient method is derived.The Fortran 77 code carried out on multivector computer Cray Y-MP implementing the algorithm above, are reported in appendix.
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